This text does refer to the first volume, but the author assures us that students who possess a “modest” background in linear algebra should be able to use this textbook. [Just in case you might need a refresher, you can refer to Volume 1 or check out the other Free Online Linear Algebra Textbooks featured on The Free Textbook List.]

This textbook is suitable for a one-semester course in vector and tensor analysis. Much of this textbook discusses Euclidean manifolds and the principle mathematical entity of fields. The authors caution that the text does not discuss “general differentiable manifolds” but “do include a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold.”